一种新的高效自适应多项式混沌展开元模型

Guangsong Chen, L. Qian, Jia Ma, Lei Ji
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引用次数: 0

摘要

为了解决元模型精度和效率方面的挑战,提出了自适应序列多项式混沌展开元模型技术(ASPCE)。使用拉丁超立方体采样(LHS)获得初始样本。针对高阶多项式混沌展开(PCE),提出了一种新的自适应截断策略,并直接利用基于PCE的Sobol灵敏度分析得到的全局灵敏度指标来更新参数。通过弹性网(EN)选择PCE的重要项,并按组合顺序准则添加样品,直至满足精度要求。因此,利用该方法可以利用少量样本构建高精度模型,并能有效地获得全局灵敏度指标。最后给出了三个基准算例和一个数值算例,验证了所提方法的有效性和高效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A new efficient adaptive polynomial chaos expansion metamodel
To address the challenge of the accuracy and efficiency of the metamodel, an adaptive sequential polynomial chaos expansion (ASPCE) metamodel technique is presented. The Latin hypercube sampling (LHS) is used to obtain the initial samples. A new adaptive truncation strategy of polynomial chaos expansion (PCE) is presented for high order PCE, and the parameters are updated by global sensitivity indices got by the Sobol' sensitivity analysis based on the PCE directly. The important terms of PCE are selected by elastic net (EN), and the samples are added according to the combined sequential criterion until the accuracy requirements are satisfied. Thus, by using the presented method, high accuracy model can be constructed by using small number of samples and the global sensitivity indices can be obtained efficiently. At last, three benchmark examples and a numerical example are provided to demonstrate the effectiveness and the efficiency of the presented method.
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